Model of change of an ejection angle in the case of penetration of an impactor into a massive target

A problem of penetration of a rigid impactor into a semi-infinite target is solved analytically to determine the dependence of the angle of expansion of ejection particles (ejection angle) on the penetration depth of the impactor. The problem is considered under the assumption of a plane deformed state of the target material. The mechanical properties of the target material are described using the hypothesis that the target material is incompressible and ideally plastic. An equation of motion (penetration) of the impactor on the basis of energy balance is obtained. The angles of ejection are determined from the condition of minimum power of internal forces. It is established that, in the case of impactor penetration to an infinite depth, the limiting value of the ejection angle (elevation angle) is approximately 84$^\circ$C.